There is no reason that some other tips would compromise your system as long as they are of the same material and quality ...
problems can arrise if you were perhaps tempted to buy really cheap tips made of acetate which cost peanuts ... neither adhesive or acrylic lasts well on these tips for several reasons ... They are very flexible and they are made with much more oil in the production which by definition neither acrylic nor EC adhesive nor the nails themselves responds well to.
So I agree with Susan in the case many brands of tips, I am pretty sure the educator would be trying to warn you against buying cheap acetate tips as I also always warned my students. The information is not actually irrelevant, it could be quite important if you chose the wrong type of tips.
To the OP and back on topic ............ the Velocity tips from CND are a fabulous tip and again for many reasons. They will fit 99% of your clients ... They have a micro contact area so normally very little tayloring needs to be done ... and they blend in a heartbeat which makes a tedious task very easy and quick ... and you can make them completely well-less if you wish by just cutting out the whole of the contact area with curved scissors which is a very quick so they are extremely versitile, and no need to buy yet another tip for that purpose ... they come in the colours of white, natural and clear and I adore using them.